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Simplifying (5x2 + -8y2) + (9x2 + -5xy + 8y2) = 0 Remove parenthesis around (5x2 + -8y2) 5x2 + -8y2 + (9x2 + -5xy + 8y2) = 0 Reorder the terms: 5x2 + -8y2 + (-5xy + 9x2 + 8y2) = 0 Remove parenthesis around (-5xy + 9x2 + 8y2) 5x2 + -8y2 + -5xy + 9x2 + 8y2 = 0 Reorder the terms: -5xy + 5x2 + 9x2 + -8y2 + 8y2 = 0 Combine like terms: 5x2 + 9x2 = 14x2 -5xy + 14x2 + -8y2 + 8y2 = 0 Combine like terms: -8y2 + 8y2 = 0 -5xy + 14x2 + 0 = 0 -5xy + 14x2 = 0 Solving -5xy + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5y + 14x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5y + 14x)' equal to zero and attempt to solve: Simplifying -5y + 14x = 0 Reorder the terms: 14x + -5y = 0 Solving 14x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 14x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 14x + 0 = 0 + 5y 14x = 0 + 5y Remove the zero: 14x = 5y Divide each side by '14'. x = 0.3571428571y Simplifying x = 0.3571428571ySolution
x = {0, 0.3571428571y}
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